Authors shortly describe the problem state about studying of discontinuous vibroimpact systems dynamical behaviour. Recently the investigations of such systems are developed rapidly. There is survey of world scientific literature about this problem. Information and description of an International Conference on Nonlinear Dynamics Complexity is given. Authors show owns the most spectacular results demonstrating the phenomena unique for nonsmooth systems describing by differential equations with discontinuous right-hand side. These results were obtained by numerical parameter continuation method.

Ajibose O. et al. Influence of contact force models on the global and local dynamics of drifting impact oscillator //Proceedings of the 8th World Congress on Computational Mechanics (WCCM’08) and 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS’08).–2008. – 2008.